$V_1(x)$ is a set of the vertices which the first bit is 1 and the remaining n-1 bits have x 1’s
$V_0(x)$ is a set of the vertices which the first bit is 0 and the remaining n-1 bits have x 1’s

---
e.g. For $n=4$
$V_1(0) =\{1000\}$, $V_1(1) =\{1100,1010,1001\}$, $V_1(2) =\{1110,1011,1101\}$, $V_1(3) =\{1111\}$

$V_0(0) =\{0000\}$, $V_0(1) =\{0100,0010,0001\}$, $V_0(2) =\{0110,0011,0101\}$, $V_0(3) =\{0111\}$

---
Simplified graph
The number next to the line is the number of multiple edges.

e.g. For $n=3$

---
$N$ means max order
initial divisior: $[N,-N,0,0,\cdots,0]$

---

$n = 2$
firing script: $[3, 0, 2, 1]$
Max order: $4$

$n = 3$
firing script: $[14, 0, 9, 5, 8, 6]$
Max order: $24$

$n = 4$
firing script: $[45, 0, 28, 17, 25, 20, 24, 21]$
Max order: $96$

etc.

=========2==========
[3, 0, 2, 1]
4
=========3==========
[14, 0, 9, 5, 8, 6]
24
=========4==========
[45, 0, 28, 17, 25, 20, 24, 21]
96
=========5==========
[372, 0, 225, 147, 202, 170, 195, 177, 192, 180]
960
=========6==========
[315, 0, 186, 129, 168, 147, 163, 152, 161, 154, 160, 155]
960
=========7==========
[3810, 0, 2205, 1605, 2004, 1806, 1953, 1857, 1934, 1876, 1925, 1885, 1920, 1890]
13440
=========8==========
[26775, 0, 15240, 11535, 13935, 12840, 13632, 13143, 13527, 13248, 13480, 13295, 13455, 13320, 13440, 13335]
107520
=========9==========
[143080, 0, 80325, 62755, 73870, 69210, 72495, 70585, 72052, 71028, 71865, 71215, 71770, 71310, 71715, 71365, 71680, 71400]
645120
=========10=========
[128898, 0, 71540, 57358, 66143, 62755, 65085, 63813, 64768, 64130, 64642, 64256, 64581, 64317, 64547, 64351, 64526, 64372, 64512, 64386]
645120
=========11=========
[1289610, 0, 708939, 580671, 658672, 630938, 649572, 640038, 647034, 642576, 646085, 643525, 645648, 643962, 645414, 644196, 645274, 644336, 645183, 644427, 645120, 644490]
7096320
=========12=========
[4729725, 0, 2579220, 2150505, 2407041, 2322684, 2378152, 2351573, 2370641, 2359084, 2368000, 2361725, 2366845, 2362880, 2366252, 2363473, 2365909, 2363816, 2365692, 2364033, 2365545, 2364180, 2365440, 2364285]
28385280
=========13=========
[113527260, 0, 61486425, 52040835, 57614130, 55913130, 57009771, 56517489, 56863016, 56664244, 56814485, 56712775, 56794350, 56732910, 56784455, 56742805, 56778932, 56748328, 56775537, 56751723, 56773290, 56753970, 56771715, 56755545, 56770560, 56756700]
738017280